Problem: Reduce to lowest terms: $ \dfrac{2}{7} \div - \dfrac{4}{9} = {?}$
Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $- \dfrac{4}{9}$ is $- \dfrac{9}{4}$ Therefore: $ \dfrac{2}{7} \div - \dfrac{4}{9} = \dfrac{2}{7} \times - \dfrac{9}{4} $ $ \phantom{ \dfrac{2}{7} \times - \dfrac{9}{4}} = \dfrac{2 \times -9}{7 \times 4} $ $ \phantom{ \dfrac{2}{7} \times - \dfrac{9}{4}} = \dfrac{-18}{28} $ The numerator and denominator have a common divisor of $2$, so we can simplify: $ \dfrac{-18}{28} = \dfrac{-18 \div 2}{28 \div 2} = -\dfrac{9}{14} $